Systems Biology

1
Systems Biology

• Ophelia Venturelli
• CS374 December 6, 2005

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Definition systems biology

• Quantitative analysis of components and dynamics
  of complex biological systems

Interactome (Tier 1)
Deterministic (Tier 2)
Stochastic (Tier 3)
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Features of complex systems

• Nonlinearity

global properties not simple sum of parts
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Features of complex systems

• Feedback loops

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Features of complex systems

• Open systems (dissipation of energy)

Flagella uses energy
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Features of complex systems

• Memory (response history dependent)

adaptation shift in curve requires memory!
Response
Chemical concentration
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Features of complex systems

• Nested (modules have complexity)

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What is Systems Biology?

• quantitatively account for these properties
• different levels of modeling
• Three tiers
• Interactomes
• Deterministic
• Stochastic
• Principles which transcend tiers

Interactome (Tier 1)
Deterministic (Tier 2)
Stochastic (Tier 3)
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Principle 1 Modularity

• Module
• interacting nodes w/ common function
• constrained pleiotropy
• feedback loops, oscillators, amplifiers

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Principle 2 Recurring circuit elements

• Network motifs
• histidine kinase response regulator

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Principle 3 Robustness

• Robustness
• insensitivity to parameter variation
• Severe constraints on design
• robustness not present in most designs

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Aims of systems biology

• Tier 1 Interactome
• Which molecules talk to each other in networks?
• Tier 2 Deterministic
• What is the average case behavior?
• Tier 3 Stochastic
• What is the variance of the system?

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Aims of systems biology

• Tier 1
• get parts list
• Tier 2 3
• enumerate biochemistry

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Aims of systems biology

• Tier 2 3
• enumerate biochemistry
• define network/mathematical relationships
• compute numerical solutions

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Aims of systems biology

• Tier 2 3
• Deterministic Behavior of system with respect to
  time is predicted with certainty given initial
  conditions
• Stochastic Dynamics cannot be predicted with
  certainty given initial conditions

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Aims of systems biology

• Deterministic
• Ordinary differential equations (ODEs)
• Concentration as a function of time only
• Partial differential equations (PDEs)
• Concentration as a function of space and time
• Stochastic
• Stochastic update equations
• Molecule numbers as random variables
• functions of time

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Tier 1 Static interactome analysis

• Protein-protein
• Signal transduction
• Cell cycle
• Protein-DNA
• Gene regulation
• Metabolic pathways
• Respiration
• cAMP

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Tier 1 Static interactome analysis

• Goals
• Determine network topology
• Network statistics
• Analyze modular structure

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Tier 1 Static interactome analysis

• Limitations
• Time, space, population average
• Crude interactions
• strength
• types
• Global features
• starting point for Tier 2 3

typical interactome
first time-varying yeast interactome (Bork 2005)
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Tier 1 Static interactome analysis

• Analysis methods
• Functional Genomics
• expression analysis
• network integration
• Graph Theory
• scale free
• small world

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Recap

• Tier 1 Interactome
• which molecules talk to each other?
• crude, large scale
• global set of modules
• Now zoom in on one module
• Tier 2 Deterministic Modeling
• average case behavior of a module

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Tier 2 Deterministic Models

• Goal
• model mesoscale system
• average case behavior
• Three levels
• ODE system
• ODE compartment system
• PDE (rare!)
• data limited

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Tier 2 Deterministic Modeling

• Results
• Robust Chemotaxis (Barkai 1997)
• MinCDE Oscillation (Howard 2003)
• Feedback in Signal Transduction (Brandman 2005)
• Output
• time series plots (ODE)
• condition on parameter values

Brandman 2005
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Tier 2 Deterministic Modeling

• Example
• Robustness in bacterial chemotaxis
• Bacterial chemotaxis robust to parameter
  fluctuations!
• Chemotaxis bacterial migration towards/away from
  chemicals
• Parameters
• concentrations
• binding affinities

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Tier 2 Deterministic Modeling

• Bacterial chemotaxis
• model as random walk
• Exact adaptation
• change in concentration of chemical stimulant
• rapid change in bacterial tumbling frequency
• then adapts back precisely to its pre-stimulus
  value!!

Random walk
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Experimental Design

• Is exact adaptation robust to substantial
  variations in biochemical parameters?
• Systematically varied concentrations of
  chemotaxis-network proteins and measured
  resulting behavior

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Distinguish between robust-adaptation and
fine-tuned models of chemotaxis
Tumbling frequency
IPTG inducer
pUA4
pUA4
Adaption time
pUA4
pUA4
E. Coli cheR -/- population
Express CheR over a 100-fold range
Adaption precision
1 mM L-aspartate
Adaptation precision ratio of steady-state
tumbling frequency of unstimulated to stimulated
cells
Summary of results
Tumbling frequency 0.3 0.06 (20-fold)
Adaption time 3 1 (3-fold)
Adaption precision 1.04 0.07
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Tumbling frequency as a function of time for
wild-type cells
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Conclusions from study

• Exact adaptation is maintained despite
  substantial varations in network-protein
  concentrations
• Exact adaptation is a robust property
• but adaptation time and steady-state behavior
  are fine-tuned

CheR fold expression
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Recap

• Just saw Tier 2
• Deterministic modeling
• average case behavior
• robustness canonical avg. case property
• Tier 3
• Stochastic modeling
• variance of system

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Tier 3 Stochastic analysis

• Fluctuations in abundance of expressed molecules
  at the single-cell level
• Leads to non-genetic individuality of isogenic
  population

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Tier 3 Stochastic Analysis

• When stochasticity is negligible, use
  deterministic modeling
• Molecular noise is low
• System is large
• molar quantities
• Fast kinetics
• reaction time negligible
• Large cell volume
• infinite boundary conditions

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Tier 3 Stochastic Analysis

• Molecular noise is high
• System is small
• finite molecule count matters
• Slow kinetics
• relative to movement time
• Large cell volume
• relative to molecule size
• Need explicit stochastic modeling!

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Tier 3 Ensemble Noise

• Transcriptional bursting
• Leaky transcription
• Slow transitions between chromatin states
• Translational bursting
• Low mRNA copy number

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Tier 3 Temporal Noise
Canonical way of modeling molecular stochasticity
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Tier 3 Spatial Noise
Finite number effect translocation of molecules
from the nucleus to the cytoplasm have a large
effect on nuclear concentration
Nucleus
Cytoplasm

• N average molecular abundance
• ? (coefficient of variation) s/N
• Decrease in abundance results ina 1/vN scaling
  of the noise (?1/vN)

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Recap

• Three tiers
• Interactomes
• Deterministic
• Stochastic
• Principles which cross tiers
• Modularity
• Reuse
• Robustness

Interactome (Tier 1)
Deterministic (Tier 2)
Stochastic (Tier 3)
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Major challenges and limitations

• Measurement of chemical kinetics parameters and
  molecular concentrations in vivo
• Differences between in vitro and in vivo data
• Compartmental specific reactions
• Data is the limit!!!

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Major challenges and limitations

• Data is the limit!!!
• Functional genomic data (Interactomes)
• E. Coli chemotaxis (Leibler, deterministic/robustn
  ess)
• Important
• parameter estimation
• feedback based estimation methods

Sachs 2005
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Software

• Tier 1 Interactomes
• Graphviz, Bioconductor, Cytoscape
• Tier 2 Deterministic
• Matlab (SBtoolbox), Mathematica (PathwayLab)
• Tier 3 Stochastic
• R, Stochsim

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Algorithms

• High-performance algorithms to solve systems of
  PDEs
• Virtual Cell
• Automated parsing of networks into stochastic and
  deterministic regimes
• H-GENESIS
• STOCK

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Conclusion

• Three tiers
• Interactomes
• Deterministic
• Stochastic
• Principles which cross tiers
• Modularity
• Reuse
• Robustness

Interactome (Tier 1)
Deterministic (Tier 2)
Stochastic (Tier 3)